Trace asymptotics for $C^{\ast }$-algebras from Smale spaces
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- by D. B. Killough and I. F. Putnam
- Proc. Amer. Math. Soc. 143 (2015), 317-325
- DOI: https://doi.org/10.1090/S0002-9939-2014-12221-0
- Published electronically: September 16, 2014
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Abstract:
We consider $C^{\ast }$-algebras associated with stable and unstable equivalence in hyperbolic dynamical systems known as Smale spaces. These systems include shifts of finite type, in which case these $C^{*}$-algebras are both AF-algebras. These algebras have fundamental representations on a single Hilbert space (subject to a choice of periodic points) which have a number of special properties. In particular, the product between any element of the first algebra with one from the second is compact. In addition, there is a single unitary operator which implements actions on both. Here, under the hypothesis that the system is mixing, we show that the (semi-finite) traces on these algebras may be obtained through a limiting process and the usual operator trace.References
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Bibliographic Information
- D. B. Killough
- Affiliation: Department of Mathematics, Physics, and Engineering, Mount Royal University, Calgary, Alberta, Canada T3E 6K6
- Email: bkillough@mtroyal.ca
- I. F. Putnam
- Affiliation: Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada V8W 3R4
- MR Author ID: 142845
- Email: ifputnam@uvic.ca
- Received by editor(s): August 24, 2012
- Received by editor(s) in revised form: April 8, 2013
- Published electronically: September 16, 2014
- Additional Notes: The second author was supported in part by an NSERC Discovery Grant
- Communicated by: Varghese Mathai
- © Copyright 2014 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 317-325
- MSC (2010): Primary 37D20; Secondary 46L55, 46L51
- DOI: https://doi.org/10.1090/S0002-9939-2014-12221-0
- MathSciNet review: 3272757